To determine the asymptote of the function \( y = 6(13)^x \), let's analyze its behavior as \( x \) approaches certain values and its general structure.
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The function \( y = 6(13)^x \) is an exponential function. Exponential functions of this form do not have vertical asymptotes, but they may have horizontal asymptotes.
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As \( x \) approaches negative infinity (\( x \to -\infty \)), \( (13)^x \) approaches zero. Therefore, \( y \) approaches zero: \[ \lim_{x \to -\infty} y = \lim_{x \to -\infty} 6(13)^x = 6 \cdot 0 = 0 \] This indicates that there is a horizontal asymptote at \( y = 0 \).
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As \( x \) increases (as \( x \to \infty \)), \( (13)^x \) increases without bound, and therefore \( y \) also increases without bound.
Given this analysis, the only correct option for an asymptote is:
B. \( y = 0 \)
This represents the horizontal asymptote where the graph approaches as \( x \) decreases.
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